arXiv 1503.026932015-03hep-phhep-exhep-lat

标准模型中的$K^+\toπ^+ν\barν$和$K_L\toπ^0ν\barν$：现状与展望

$K^+\toπ^+ν\barν$ and $K_L\toπ^0ν\barν$ in the Standard Model: Status and Perspectives

Andrzej J. Buras, Dario Buttazzo, Jennifer Girrbach-Noe, Robert Knegjens

备注：: 33 pages, 8 figures, 5 tables; v2: new correlation presented and discussion extended in section 3.2, analysis in section 5 updated, typos corrected; matches version published in JHEP
发表信息：: JHEP 1511 (2015) 033
DOI：: 10.1007/JHEP11(2015)033

摘要：

鉴于最近开始的NA62实验在欧洲核子研究中心，预计测量$K^+\toπ^+ν\barν$分支比的精度为10%，我们总结了目前的状况，这种有前途的衰变内的标准模型（SM）。我们对密切相关的$K_L\toπ^0ν\barν$也做了同样的处理，它将在2020年左右由KOTO实验测量。由于微扰QCD和电弱修正在这两个衰变的完全控制下，占主导地位的不确定性SM目前来自CKM参数$V_{cb}$，$V_{ub}$和$γ$。我们表明这种依赖关系的帮助下，解析表达式以及准确的插值公式。不幸的是，要澄清$V_{cb}$和$V_{ub}$在树级衰变中的包容性和排他性测定之间的差异，可能需要在本世纪末获得Belle II实验的结果。因此，我们调查是否更高的精度上的两个分支比是通过确定$V_{cb}$，$V_{ub}$和$γ$通过其他已经精确测量的可观的。在这种情况下，$\varepsilon_K$和$ΔM_{s,d}$，以及QCD晶格计算的预期进展将发挥突出的作用。我们找到了$\mathcal{B}(K^+\toπ^+ν\barν) = (9.11\pm 0.72) \times 10^{-11}$和$\mathcal{B}(K_L\toπ^0ν\barν) = (3.00\pm 0.30) \times 10^{-11}$，这比使用$V_{cb}$，$V_{ub}$和$γ$的当前树级值的平均值更精确。此外，我们指出的相关性$\mathcal{B}(K^+\toπ^+ν\barν)$，$\overline{\mathcal{B}}(B_s\toμ^+μ^-)$和$γ$的SM内，这是非常弱的依赖于其他CKM参数。最后，我们还更新了SM中的比率$\varepsilon'/\varepsilon$，并呈现其与$K_L\toπ^0ν\barν$的相关性。

英文摘要：

In view of the recent start of the NA62 experiment at CERN that is expected to measure the $K^+\toπ^+ν\barν$ branching ratio with a precision of 10%, we summarise the present status of this promising decay within the Standard Model (SM). We do likewise for the closely related $K_L\toπ^0ν\barν$, which will be measured by the KOTO experiment around 2020. As the perturbative QCD and electroweak corrections in both decays are under full control, the dominant uncertainties within the SM presently originate from the CKM parameters $V_{cb}$, $V_{ub}$ and $γ$. We show this dependence with the help of analytic expressions as well as accurate interpolating formulae. Unfortunately a clarification of the discrepancies between inclusive and exclusive determinations of $V_{cb}$ and $V_{ub}$ from tree-level decays will likely require results from the Belle II experiment available at the end of this decade. Thus we investigate whether higher precision on both branching ratios is achievable by determining $V_{cb}$, $V_{ub}$ and $γ$ by means of other observables that are already precisely measured. In this context $\varepsilon_K$ and $ΔM_{s,d}$, together with the expected progress in QCD lattice calculations will play a prominent role. We find $\mathcal{B}(K^+\toπ^+ν\barν) = (9.11\pm 0.72) \times 10^{-11}$ and $\mathcal{B}(K_L\toπ^0ν\barν) = (3.00\pm 0.30) \times 10^{-11}$, which is more precise than using averages of the present tree-level values of $V_{cb}$, $V_{ub}$ and $γ$. Furthermore, we point out the correlation between $\mathcal{B}(K^+\toπ^+ν\barν)$, $\overline{\mathcal{B}}(B_s\toμ^+μ^-)$ and $γ$ within the SM, that is only very weakly dependent on other CKM parameters. Finally, we also update the ratio $\varepsilon'/\varepsilon$ in the SM and present its correlation with $K_L\toπ^0ν\barν$.

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